Temperature-independent antilogarithm circuit

ABSTRACT

A circuit for obtaining an output voltage proportional to the antilogarithm of an input voltage. The circuit is made insensitive to temperature variations by constructing its two transistors as an integrated structure on the same substrate so that they are made of the same materials, by the same process and with a very close thermal coupling. This construction insures that all the critical parameters of the transistors, particularly the ratio of the reverse saturation currents of the base-emitter junctions, are stabilized against temperature changes.

United States Patent lnventor Richard L. Moose Burlington, N.C.

Appl. N0. 767,979

Filed Oct. 16, 1968 Patented Oct. 12, 1971 Assignee Bell TelephoneLaboratories, Incorporated Murray Hill, NJ.

TEMPERATURE-INDEPENDENT ANTlLOGARITl-IM CIRCUIT 6 Claims, 2 DrawingFigs.

U.S. Cl 307/229, 307/310, 328/145, 307/303 Int. Cl 606g 7/24 Field ofSearch 307/310,

References Cited UNITED STATES PATENTS Platzer 3,308,271 3/1967Fi'iiEibi 307/310 3,393,328 7/1968 Meadows.... 307/310 3,395,265 7/1968Weir 307/310 3,444,362 5/1969 Pearlman 328/145 3,089,968 5/1963 Dunn328/145 Primary Examiner-Donald D. Forrer Assistant Examiner-Harold A.Dixon Attorneys-R. J. Guenther and William L. Keefauver ABSTRACT: Acircuit for obtaining an output voltage proportional to theantilogarithm of an input voltage. The circuit is made insensitive totemperature variations by constructing its two transistors as anintegrated structure on the same substrate so that they are made of thesame materials, by the same process and with a very close thermalcoupling. This construction insures that all the critical parameters ofthe transistors, particularly the ratio of the reverse saturationcurrents of the base-emitter junctions, are stabilized againsttemperature changes.

PATENTEUUET 12 Ian wvuvron R. L. MOOSE BY "Z/Amb 14 My -AMP A T TOPNEYTEMPERATURE-INDEPENDENT AN'IILOGARITHM CIRCUIT GOVERNMENT CONTRACTS Theinvention herein claimed was made in the course of, or under contractwith the Department of the Army.

BACKGROUND OF THE INVENTION This invention relates to the art ofelectrical calculation and more particularly to atemperature-independent antilogarithmic circuit.

While the characteristics of many solid-state devices are quitepredictable, one of the defects inherent in most prior artantilogarithmic circuits using transistors is thermal drift which causesthe output to vary as a function of temperature changes. This thermaldrift usually created an intolerable error in the output circuit and wasgenerally corrected by placing the transistors in thermally regulatedovens. This, of course, increases the size, weight and cost of thecircuit, all of which are undesirable consequences of the need toeliminate the error due to thermal drift. The source of this drift errorresides in the fact that the emitter current of a transistor is directlyproportional to the saturation current through its base-emitter junctionand since the saturation current can change by a ratio of 2:1 for eachtemperature change of 7 C., the emitter current will also change by thesame ratio. Consequently, any circuit based on the absolute magnitude ofthe emitter current will be highly unstable with temperature.

SUMMARY OF THE INVENTION Stability against the effect of thermal driftsover a wide temperature range is achieved by this invention by meansproviding a close thermal coupling between two transistors of the sametype which are closely matched both in materials and in theirfabrication process. The base and collector of the first transistor aredirectly connected to the base of the second transistor and to one poleof a direct-voltage power source through a resistor while its emitter isconnected to the other pole of the power source. A second resistorconnects the collector of the second transistor to the power source. Theinput signal is supplied to the emitter of the second transistor from alow-impedance source while the antilogarithm output is taken from itscollector. Because of the close thermal coupling and matching, the ratioof their base-emitter junction saturation currents will remainsubstantially constant, although these currents themselves vary greatlywith temperature.

BRIEF DESCRIPTION OF THE DRAWINGS The invention may be better understoodby a reference to the accompanying drawings in which:

FIG. I is a circuit diagram disclosing the essential features of apreferred embodiment of the invention; and

FIG. 2 shows the basic transistor circuit useful in explaining theoperation of the invention.

DETAILED DESCRIPTION The circuits of a preferred embodiment of theinvention are disclosed in FIG. 1 which shows a pair of transistors Q1and Q2 of the same type which are thermally coupled through a thermallink 6. The two transistors should not only be of the same type but theyshould be closely matched as to the materials of which they areconstructed and it is essential that they be closely coupled through thethermal path provided by the thermal link 6. Preferably, these twotransistors are constructed of the same materials on a single, thermallyconductive substrate which may comprise the thermal link 6. Under thesecircumstances, the materials of which the two transistors areconstructed will be practically identical and they will be identicallyprocessed using integrated circuit techniques, thereby resulting in avery close material match. The emitter of transistor O1 is groundedwhile its base and collector are both ioined to one terminal of resistorR the other terminal of which is connected to a source of direct voltage+E. The bases of the two transistors are directly connected togetherwhile the collector of transistor O2 is connected to the direct voltagesource through a resistor R, The emitter of transistor 02 is connectedto ground through a very low impedance signal source provided by theoutput circuit of operational amplifier 3. The signal voltage e isapplied between input terminal 1 and ground, input terminal 1 beingconnected to the input circuit of operational amplifier 3. Signalvoltage e is preferably obtained from a commercially availablelogarithmic amplifier circuit 10 to which is applied an input voltage eThe output circuit of operational amplifier 3 is connected to theemitter of transistor Q2 by way of conductor 5. The output terminal 2 ofthe circuit, from which the antilogarithm is obtained, is connected tothe collector of transistor 02.

The operational amplifier 3 is of conventional construction having ahigh gain amplifier means 4 with feedback and input resistors R, and Rrespectively. The configuration is of conventional design and it is tobe understood that its gain and feedback are such as to provide theamplifier circuit with a very low output circuit impedance. This isparticularly true where resistor R is made very large, approachinginfinity. In this case, the output impedance of the amplifier willclosely approximate the impedance of its output stage divided by theforward gain of the amplifier means 4.

With the circuit as shown in FIG. I, a signal voltage e applied betweeninput terminal 1 and ground will produce an output voltage 2,, betweenoutput terminal 2 and ground which is proportional to the antilogarithmof the signal voltage. Moreover, it can be shown that so long as the twotransistors are of the same type and are closely matched both inmaterials and in their fabrication process and so long as they are veryclosely thermally coupled, the circuit will be virtually independent oftemperature changes over a very wide temperature range.

The manner by which this circuit provides thennal stability may be morefully understood by reference to FIG. 2 which discloses the transistorcircuits of FIG. I in which the operational amplifier 3 has been shownto comprise an output stage impedance R, in series with a generatorvoltage V, and an offset direct voltage V,. The generator voltage V, isactually a very close approximation of the input signal voltage eapplied to input terminal 1. Currents I, and i,, flowing through theirrespective collector resistors R and R,, very closely approximate theemitter currents of their associated transistors 01 and Q2. Theemitter-to-base voltage of transistor 01 is shown by the small arrowlabeled V, while the emitter-to-base voltage of transistor 02 issimilarly shown as V,,,. The voltage equation for the mesh comprisingthe two base-emitter junctions and the operational amplifier is:

b 3bl 9 i o l It remains to be shown that the emitter current oftransistor Q2 is proportional to the antilogarithm of the voltage V,.This can best be shown by first considering the well known diode lawwhich applies to the base-emitter junctions of both transistors. Thislaw is expressed as follows:

where:

i= junction current I reverse saturation current e base of naturallogarithms q electronic charge N constant of material K Boltzmann'sconstant T= temperature-degrees Kelvin V= voltage across junctionExpression (2) may be solved for the junction voltage and may beexpressed by the very close approximation given below, which is obtainedfrom expression (2) by noting that the ratio of the junction current tothe saturation current is very large compared with unity when thejunction is in its forward conducting region.

U/M U/ Now by combining expressions (1 and (3) the following expressionfor the emitter current of transistor Q2 is obtained:

' i ..i*, tiff i i5; if)

where:

i,=(E0.7 )/R a constant,

e. 0.9 over a wide temperature range and f' z l where R, is made small.The initter current i of transistor O1 is essentially constant as isalso the product of the two exponential functions included in theparenthesis in expression (4). The first exponential function closelyapproximates 0.9 for a very wide temperature range extending at leastfrom C. to 100 C. The value of 0.9 is obtained when the materialconstant N is approximately 1.5, as is true for silicon junctions, andthe offset voltage V approximates millivolts. The second exponentialfunction closely approximates unity because the output impedance R, ofthe amplifier is made very small. The ratio of the saturation currents(I /I can be made constant provided that the transistors are of the sametype, made of the same materials, fabricated by the same process andmaintained at equal temperatures. In accordance with the presentinvention, this is preferably accomplished by forming the twotransistors of the same materials on a single substrate. When this isdone, the output current i may be expressed as follows:

i As:

where:

A the product of the constant emitter current i and the quantitiescontained in parentheses in expression (4).

Although the output current i is also a function of temperature becausethe expression for A contains a temperature parameter, the circuit isseveral orders of magnitude more stable than it would be if the twotransistors were not constructed as described above and kept at equaltemperatures. In a practical circuit, the logarithmic amplifier circuitis preferably of the type described in Fairchild Application BulletinAPP-124, Jan. 1966, FIG. 3 in which transistors and operationalamplifiers are also used for deriving an output voltage which is thelogarithm of its input signal voltage. Thus, in FIG. 1, the outputvoltage e from logarithmic amplifier 10 is proportional to the logarithmof the input signal voltage a, applied between input terminal 11 andground. It will be evident to those skilled in this art that if two suchlogarithmic amplifiers are used and their outputs summed at terminal 1of FIG. 1, the product (or quotient) of their two input signal voltagesmay be derived. Moreover, if the gain of logarithmic amplifier 10 ismade other than unity, its output voltage e will vary as the logarithmof a power or root of the input signal voltage e For example, if thegain of logarithmic amplifier 10 is made 1/2, the output voltage e atterminal 2 will vary as the square root of the input signal voltage e,at terminal 11. Now, in accordance with the present invention, if thematched transistors in the logarithmic amplifier 10 are made in the sameway as are transistors Q1 and Q2 of FIG. 1, and particularly if they arefabricated on the same substrate as are transistors Q1 and Q2,substantially complete temperature compensation is achieved. When thisconstruction is used, the input voltage e for the linear case, which issubstantially equal to voltage V can be written as:

where: k is an arbitrary constant determined by the component parametersof logarithmic amplifier 10.

Combining expressions (5) and (6) causes the A parameters to cancel sothat:

i =A ke, (7)

Similar considerations will show that for the cases where powers,products or quotients are obtained, the A parameters still cancel toprovide excellent temperature compensation without the need for aconstant temperature oven.

While the invention has been described with reference to a specificembodiment, it will be apparent to those skilled in this art thatvarious modifications may be made without departing from the scope ofthe invention.

What is claimed is: l. A temperature-independent antilogarithmlc circuitresponsive to applied input signals comprising first and second closelymatched transistors of the same type, each having a collector, a baseand an emitter, said transistors being closely coupled through a thermalpath, both the collector and the base of said first transistor beingdirectly connected to the base of said second transistor; means forapplying said input signals to the emitter of said second transistor,said input signals being applied with respect to a ground referencepotential, said means for applying said input signals comprising alow-impedance signal source having first and second terminals, means forconnecting the first of said terminals to the emitter of said secondtransistor, and means for maintaining the second of said terminals atsaid ground reference potential, said low impedance source comprisingthe output circuit of an operational amplifier having sufficientfeedback to provide a very low output circuit impedance compared withits output circuit impedance without feedback; and means for maintainingthe emitter of said first transistor at said ground reference potentialso that output signals representative of the antilogarithm of said inputsignals appear at the collector of said second transistor.

2. The combination of claim 1 and a logarithmic amplifier having anoutput connected to supply a signal voltage to said operationalamplifier.

3. A temperature-independent circuit for generating output signalsrepresentative of the antilogarithm of applied input signals comprisingfirst and second closely matched transistors of the same type, eachhaving a collector, a base and an emitter, means maintaining a closethermal coupling between said two transistors, means directly connectingboth the collector and the base of the first transistor to the base ofthe second transistor, a source of direct voltage having first andsecond poles, means directly connecting the first of said poles to theemitter of said first transistor, first and second resistorsrespectively connecting the collectors of said first and secondtransistors to the second of said poles of said direct voltage source,means for applying said input signals between the emitter of said secondtransistor and the first of said poles of said direct voltage source,and an output terminal connected to the collector of said secondtransistor so that said output signals representative of theantilogarithm of said applied input signals appear at said outputterminal.

4. The combination of claim 1 wherein said means maintaining a closethermal coupling comprises a single substrate upon which both of saidtransistors are formed into an integrated structure.

5. The combination of claim 1 wherein said means for applying said inputsignals comprises a low-impedance signal source connected between theemitter of said first transistor and the first of said poles of saiddirect voltage source, said low-impedance source comprising the outputcircuit of an operational amplifier having sufficient feedback toprovide a very low output circuit impedance compared with its outputcircuit impedance without feedback.

6. The combination of claim 5 and a logarithmic amplifier having anoutput connected to supply a signal voltage to said operationalamplifier.

UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No. 3, 12,92 Dated October 12, 1971 lnv tofl Richard L. Moose It is certified thaterror appears in the above-identified patent and that said LettersPatent are hereby corrected as shown below: K

H H a Column 2, line #8, change V to --V line 52, change Equation (1)from H V8132 V3101 V9 V R 1 to eb2 ebi o i 0 line 7'5, change Equation(3 from "v (1/7\)1n(i/I to Column 3, line 59, change Equation (6 from eV (1/7\)1n ke to Column LL, line 51, claim A change "1" to --3--; line55, claim 5 change "1" to --3--.

Signed and sealed this 6th day of June 1972.

(SEAL) Attest:

EDWARD M.FLETCHER,JR. ROBERT GO'ITSCHALK Attesting Officer Commissionerof Patents )RM PO-IOBO (10-69) USCOMM DC some-p69 U 5 GOVERNMENTPRINYING OFFICF Q59 O.'HvB*1J4

1. A temperature-independent antilogarithmic circuit responsive toapplied input signals comprising first and second closely matchedtransistors of the same type, each having a collector, a base and anemitter, said transistors being closely coupled through a thermal path,both the collector and the base of said first transistor being directlyconnected to the base of said second transistor; means for applying saidinput signals to the emitter of said second transistor, said inputsignals being applied with respect to a ground reference potential, saidmeans for applying said input signals comprising a low-impedance signalsource having first and second terminals, means for connecting the firstof said terminals to the emitter of said second transistor, and meansfor maintaining the second of said terminals at said ground referencepotential, said low impedance source comprising the output circuit of anoperational amplifier having sufficient feedback to provide a very lowoutput circuit impedance compared with its output circuit impedancewithout feedback; and means for maintaining the emitter of said firsttransistor at said ground reference potential so that output signalsrepresentative of the antilogarithm of said input signals appear at thecollector of said second transistor.
 2. The combination of claim 1 and alogarithmic amplifier having an output connected to supply a signalvoltage to said operational amplifier.
 3. A temperature-independentcircuit for generating output signals representative of theantilogarithm of applied input signals comprising first and secondclosely matched transistors of the same type, each having a collector, abase and an emitter, meanS maintaining a close thermal coupling betweensaid two transistors, means directly connecting both the collector andthe base of the first transistor to the base of the second transistor, asource of direct voltage having first and second poles, means directlyconnecting the first of said poles to the emitter of said firsttransistor, first and second resistors respectively connecting thecollectors of said first and second transistors to the second of saidpoles of said direct voltage source, means for applying said inputsignals between the emitter of said second transistor and the first ofsaid poles of said direct voltage source, and an output terminalconnected to the collector of said second transistor so that said outputsignals representative of the antilogarithm of said applied inputsignals appear at said output terminal.
 4. The combination of claim 1wherein said means maintaining a close thermal coupling comprises asingle substrate upon which both of said transistors are formed into anintegrated structure.
 5. The combination of claim 1 wherein said meansfor applying said input signals comprises a low-impedance signal sourceconnected between the emitter of said first transistor and the first ofsaid poles of said direct voltage source, said low-impedance sourcecomprising the output circuit of an operational amplifier havingsufficient feedback to provide a very low output circuit impedancecompared with its output circuit impedance without feedback.
 6. Thecombination of claim 5 and a logarithmic amplifier having an outputconnected to supply a signal voltage to said operational amplifier.